One-dimensional Wave Research Articles

To simple waves and small-amplitude perturbations in radiation gasodynamics

The paper analyzes one-dimensional simple waves and small-amplitude perturbations in radiating and scattering gray gas. The governing equation of radiation acoustics describing the dynamics of simple waves is derived. The conditions of radiation-thermal dissipation and radiation resistance force are introduced into this equation to describe the propagation with dissipation and attenuation of various radiation perturbation waves. The phenomenological approximate Whitham method is used to investigate non-equilibrium wave phenomena in radiative medium. This method is an effective way to analyze fundamental modes when more than one velocity appears in the governing equation. The use of this method is demonstrated in this paper by considering the evolution of one-dimensional harmonic waves caused by a short-wave initial perturbation of the equilibrium state of the radiating and scattering medium. Analytical solutions are obtained for all wave modes, which allow us to interpret their physical meaning. These solutions can be, in particular, an additional test for radiative hydrodynamic codes operating in the radiative acoustics regime. The presented approach may be useful in detailing higher-order numerical Godunov schemes for radiation acoustics problems.

Phononic band calculations and experimental imaging of topological boundary modes in a hexagonal flexural wave machine

We construct a two-dimensional mechanical wave machine based on a hexagonal lattice to investigate low-frequency flexural plate waves whose propagation mimicks a topological quantum valley Hall system. We thereby demonstrate “mechanical graphene” by extension of the one-dimensional Shive wave machine to two dimensions. Imaging experiments, backed up by simulations, reveal the presence of boundary modes along a topological interface. This work provides an alternative route for the investigation of topological phononic crystals, and should lead to new insights into the design and observation of artificial phononic structures.

Линейное тестирование некоторых разностных схем МГД

One-dimensional linear wave testing has been performed for some numerical techniques for solution of the ideal magnetohydrodynamic system of equations. The mesh-characteristic method is under consideration as well as the numerical technique implemented in the software package MARPLE. The results are compared with the results of the similar tests performed for the schemes implemented in Athena code (Roe, HLLD, HLLE). Our schemes demonstrate values of the norm of the numerical solution error for propagation of the low-amplitude (linear) MHD-waves which are comparable with the numerical techniques implemented in Athena code.

A priori estimates for derivative solutions of one-dimensional inhomogeneous wave equations with an integral load in the main part

A priori estimates for derivative solutions of one-dimensional inhomogeneous wave equations with an integral load in the main part

One-dimensional thermo-elastic wave analysis for dynamic thermoelasticity coupled with dual-phase-lag heat conduction model

One-dimensional thermo-elastic wave analysis for dynamic thermoelasticity coupled with dual-phase-lag heat conduction model

General concept for autoignitive reaction wave covering from subsonic to supersonic regimes

We consider a one-dimensional (1D) autoignitive reaction wave in a reactive flow system comprising unburned premixed gas entering from the inlet boundary and burned gas exiting from the outlet boundary. In such a 1D system at given initial temperature, it is generally accepted that steady-state solutions can only exist if the inlet velocity matches either the velocity of deflagration wave, as determined by the burning rate eigenvalue in the subsonic regime, or the velocity of detonation wave as dictated by the Chapman–Jouguet condition in the supersonic regime. Based on our recently published theory that ignition is equivalent to deflagration wave with unity Lewis number, we believe that it is possible to redefine deflagration wave from ignition. Thus, we have developed the general concept of “autoignitive reaction wave” and shown theoretically that there are two distinct regions that can maintain steady-state solutions in both the subsonic and supersonic regimes. Based on this theory, we selected inlet velocities that are predicted to yield either steady-state or flashback solutions and conducted numerical simulations. This novel approach revealed that steady-state solutions are possible not only at the velocity of the deflagration wave in the subsonic regime and the velocity of the detonation wave in the supersonic regime, but also across a broad range of inlet velocities. Furthermore, we identify a highly stable autoignitive reaction wave that emerges when the inlet velocity surpasses the velocity of detonation wave, devoid of the typical shock wave commonly seen in detonation waves. This “supersonic autoignitive reaction wave” lacks the instability-inducing detonation cell structure, suggesting the potential for the development of novel combustor concepts.

Substructure elimination and binding method for vibration systems governed by a one-dimensional wave equation

Substructure elimination and binding method for vibration systems governed by a one-dimensional wave equation

Numerical method for restoring the initial condition for the wave equation

The inverse problem of restoring the initial condition for the time derivative for the one-dimensional wave equation is considered. As an additional condition, the solution of the wave equation at a finite time is given. First, the discretization of the derivative with respect to the spatial variable is carried out and the initial problem is reduced to a differential-difference problem with respect to functions depending on the time variable. To solve the resulting differential-difference problem, a special representation is proposed, with the help of which the problem splits into two independent differentialdifference problems. As a result, an explicit formula is obtained for determining the approximate value of the desired function for each discrete value of a spatial variable. The finite difference method is used for the numerical solution of the obtained differentialdifference problems. The presented results of numerical experiments conducted for model problems demonstrate the effectiveness of the proposed computational algorithm.

Acoustic Modeling and Analysis of Automotive Air-Filters

Air filters are placed upstream of internal combustion engines to remove dust particles in the suction air. In this article, we examine the acoustic characterization of an air-filtering unit in the absence of mean flow. For this purpose, a circular air-filtering unit with an axial inlet and side outlet widely used in the automobile industry is considered. The air-filter element is modeled as an equivalent acoustic fluid with finite flow resistivity. The flow resistivity of the region is estimated from the permeability of the filter paper and the geometrical arrangement of the paper folds (pleats) inside the air-filter element using an electrical analogy. A numerical model based on the finite element method (FEM) and an analytical model using classical one-dimensional plane wave analysis (1-D PWA) was developed. Experiments were carried out using an impedance tube to estimate transmission loss. A good correlation is observed between the FEM model and the experiments. The results obtained from the 1-D PWA are in reasonable agreement with those obtained from the other two methods.

INFORMATIVENESS OF TRANSIENT AND TWO-DIMENSIONAL SHEAR WAVE ELASTOGRAPHY IN ASSESSING OF LIVER STIFFNESS IN POST-COVID-19 AND CARDIOHEPATIC SYNDROMES

Ultrasound elastography of diffuse liver diseases allows to assess liver stiffness and predict the further course of the disease, determine the tactics of patient’s management for post-Covid and cardiohepatic syndrome. The purpose of the research – to study the diagnostic informativeness and evaluate the correlation between one-dimensional and two-dimensional shear wave elastography technologies with elastometry in assessing liver stiffness in patients with post-COVID and cardiohepatic syndromes. Materials and methods. A comparative analysis of the information content and correlation between the results of one-dimensional and two-dimensional shear wave elastography of the liver was carried out in 85 patients with post-COVID (N1; n = 30) and cardiohepatic (N2; n = 25) syndromes. The control group (N3; n = 30) consisted of patients without the new coronavirus infection COVID-19 and without any pathology of the liver and biliary system. In the control group, the study of liver parenchyma stiffness using shear wave elastography was carried out by lobes and segments. Standard variation statistics algorithms were used, taking into account the type of data distribution in the statistical analysis. Quantitative indicators with a normal distribution were described using arithmetic means (M) and standard deviations (SD), boundaries of the 95% confidence interval (95% CI). In the absence of a normal distribution, quantitative data were described using the median (Me) and lower and upper quartiles (Q1–Q3). Research results. The stiffness values (Emean) in the projection of segments VI, VII had larger values (p = 0.02) when compared with other segments. We obtained the following Emean values in transient elastography: in the group of patients with post-COVID syndrome (N1) – 10.02 kPa; in the group of patients with chronic heart failure (N2) – 14.09 kPa, which turned out to be significantly higher than the stiffness of the liver parenchyma among healthy individuals, where the Emean value was 4.90 kPa (p = 0.05). With shear wave elastography, the results were also higher in the group of patients with chronic heart failure (N2), where Emean was 20.90 kPa, compared to the group of patients with post-COVID syndrome (N1) – 11.86 kPa. Conclusions. The results of shear wave elastography were successful in 100% of cases, the results of transient elastography in 84.6% of cases. Correlation analysis of connections in a group of patients with chronic heart failure according to TE and SWE showed a weak positive direct linear correlation. A positive direct linear correlation of medium strength was obtained in assessing the correlation in the group of patients with post-COVID syndrome.

Wave measurements using open source ship mounted ultrasonic altimeter and motion correction system during the one ocean circumnavigation

This study reviews the design and signal processing of ship borne ultrasonic altimeter wave measurements. The system combines a downward facing ultrasonic altimeter to capture the sea surface elevation as a time series, and an inertial measurement unit to compensate for the ship’s motion. The methodology is cost-effective, open source, and adaptable to various ships and platforms. The system was installed on the barque Statsraad Lehmkuhl and recorded data continuously during the 20-month One Ocean Expedition. Results from 1-month crossing of the Tropical Atlantic are presented here. The one-dimensional wave spectrum and associated wave parameters are obtained from the sea surface elevation time series. The observed significant wave height agrees well with satellite altimetry and a spectral wave model. The agreement between observations and the spectral wave model is better for the mean wave period than the peak period. We perform Doppler shift corrections to improve wave period estimates by accounting for the speed of the ship relative to the waves. This correction enhances the accuracy of the mean period, but not the peak period. We suggest that the Doppler correction could be improved by complementing the data sources with directional wave measurements from a marine X-band radar.

Hydrodynamic performance of an elastic capsule oscillating water column type WEC: An experimental study

Wave energy represents a promising and sustainable source of energy with substantial potential. To promote the utilization of wave energy resources as well as develop new wave energy converters (WECs) with application prospects, an innovative elastic capsule oscillating water column (EC-OWC) WEC is proposed, and an initial experimental investigation is conducted on the device. Besides, the expansion characteristics of the elastic capsule and the motion characteristics of the free bulge wave are investigated through bulge wave tests. Moreover, the hydrodynamic performances of the device on the condition that coupled with traveling regular waves are investigated through wave tests, as well as the damping characteristics of the impulse turbine model and the ring-opening as power take-off (PTO) systems in the EC-OWC. It indicates that the variation in the speed of the free bulge wave is consistent with the one-dimensional longitudinal wave theory, that the ring-opening model with an opening ratio of 0.76 percent has comparable operating characteristics to the impulse turbine, and that the impulse turbine model has outstanding operating characteristics in the EC-OWC system. The maximum primary hydrodynamic efficiency of the system is approximately 0.475. When the relative water depth is in the interval of approximately 0.07-0.09, the efficiency can reach 0.4. Furthermore, the efficiency increases and subsequently decreases with the variation of the relative hydraulic head, and the efficiency reaches the maximum value when the relative tube length is around 1.6. The results indicate that the one-dimensional longitudinal wave theory can provide support for the design of the elastic capsule. When the capsule length is close to half a wavelength and the internal and external oscillation periods are matched, the system reaches a near-resonant state, and the level of efficiency is optimized. The bulge wave contained within the EC-OWC is a half-wavelength standing wave.

A High-Order Immersed Moving Boundary Method Using Ghost Points and Characteristics for Acoustics

Realistic acoustic problems often involve interactions between arbitrary-shaped moving objects at the interface with a fluid domain. The present work aims at developing numerical methods to take into account moving boundaries for acoustic problems, with a high order of convergence. The reference problem considered in this work is the solution of the non-linear Euler equations by a finite-difference time-domain method, describing the formation of one-dimensional waves created by a moving piston. The most suitable class of methods to solve this type of problem in the case of complex moving boundaries is the ghost-point method for sharp interface with 4th order reconstruction. 1 In order to accurately formulate the immersed boundaries with ghost points, the boundary conditions are formulated in terms of characteristic waves of the non-linear equations. The proposed approach is also extended to represent moving boundaries with a prescribed acoustic impedance. This is achieved by coupling a time-domain acoustic impedance model to the immersed boundary technique. The method is also applied to a two-dimensional example, where an acoustic pulse is reflected by a moving wall.

Elastic wave propagation in a porous composite with gradient porosity

Wave propagation in gradient porous composite exhibits more complex dynamic behavior than its propagation in non-gradient porous composite due to the spatial variation of mechanical properties. There is a lack of adequate theoretical model that can be used to provide efficient and accurate analyses of the wave propagation in a gradient porous composite. To address this issue, this paper develops a novel analytical technique to study the propagation of one-dimensional elastic wave with relatively low frequency components in a gradient porous composite. The governing wave equation considering the scattering effect caused by cavities is employed to describe the wave propagation in a porous composite. In order to consider the porosity gradient of the composite, a segmented model is constructed to formulate the wave propagation in porous composite by combining the reverberation matrix method and stress wave solution with considering the wave scattering in Rayleigh scattering region. Meso-scale finite element simulations are conducted to validate the proposed method and investigate the effect of the randomness of cavity's spatial distribution. The valid conditions of wavelength and porosity for the present method are determined by quantitative comparison and qualitative analysis, which provides a better understanding about the basis of macroscopic wave propagation. Finally, a parametric analysis is carried out to investigate the effects of porosity gradient on the wave propagation behavior.

Investigation on the Utilization of Millimeter-Wave Radars for Ocean Wave Monitoring

The feasibility of using millimeter-wave radars for wave observations was investigated in this study. The radars used in this study operate at a center frequency of 77.572 GHz. To investigate the feasibility of wave observations and extract one-dimensional and two-dimensional wave spectra, arrays consisting of multiple radar units were deployed for observations in both laboratory and field environments. Based on the data measured with the millimeter-wave radars, one-dimensional wave spectra and two-dimensional wave directional spectra were evaluated using the periodogram method and the Bayesian directional spectrum estimation method (BDM), respectively. Meanwhile, wave parameters such as the significant wave height, wave period, and wave direction were also calculated. Via comparative experiments with a capacitive wave height meter in a wave tank and RADAC’s WG5-HT-CP radar in an offshore field, the viability of using millimeter-wave radars to observe water waves was validated. The results indicate that the one-dimensional wave spectra measured with the millimeter-wave radars were consistent with those measured with the mature commercial capacitive wave height meter and the WG5-HT-CP wave radar. Via wave direction measurement experiments conducted in a wave tank and offshore environment, it is evident that the wave directions retrieved with the millimeter-wave radars were in good alignment with the actual wave directions.

Specific Point in Time Excitation Control Method for Spatial Multi-Degree-of-Freedom Systems under Continuous Operation

The port container gantry crane studied in this paper is a four-degree-of-freedom spatial continuous system. In actual work, in order to make the container transfer smoothly, the response of the whole system needs to be accurately predicted and timely adjusted. The whole system is divided into rotary mechanism, lifting mechanism, lifting trolley mechanism, and big cart mechanism for detailed analysis. By constructing the field transfer matrix, a one-dimensional wave equation of continuous system and the Lagrange equation with redundant parameters, the response of each subsystem is solved precisely. The results of the study found that in some periods, the swing of the container was too large. In order to improve the safety and stability of transmission, an active control method of specific point in time excitation (SPE) is proposed for the first time. This method predicts the swing amplitude of the container in advance using the response results of the numerical model. When the set response interval is exceeded, the external excitation intervention can effectively inhibit the moving range of the container in the transit process. Finally, the results are compared with the simulation model to achieve the experimental purpose. It is in line with the expected experimental effect.

Practical tutorial on cylindrical structure vibro-acoustics Part 2 - Acoustics

In part 1 of this tutorial (proceedings of Inter-noise 2022) I explained vibrations in cylindrical shell structures. In that paper I limited the mathematics and focused on the key behavior of shells based on critical parameters like the ring frequency, helical wavenumbers, and mean mobilities over different frequency ranges. I compared measured data to the simple theories. In part 2, I focus on the acoustics of cylindrical shells, including sound within shells and the sound radiated outside them. Exterior sound radiation depends strongly on the circumferential order of the shell modes. Breathing modes near the ring frequency radiate sound extremely well, but have very high impedances, so can be difficult to excite. Beam-like modes, where the entire shell cross-section vibrates transversely, radiate less efficiently, but can be easily driven. Higher order, or 'lobar' modes radiate even less efficiently, but nevertheless are commonly observed in radiated sound spectra due to their low impedances. I also review statistical estimates of radiation efficiency of groups of shell modes, which show clear peaks at both the ring frequency as well as at the critical frequency of bending waves. The mathematics of sound inside cylindrical shells is some of the most challenging in vibro-acoustics. At low frequencies, however, the interior sound is dominated by simple one-dimensional planar acoustic waves. At higher frequencies, the sound depends on how well a shell vibration field matches the interior acoustic field based on proximity of resonance frequencies and the similarity of mode shape orders, as well as the 'cut on' frequencies of higher order internal acoustic modes. Finally, I review the well-known phenomenon of how a low shell wall impedance can reduce the effective acoustic sound speed of one-dimensional waves inside cylindrical shells.

Track-bridge deformation relation and interaction of long-span railway suspension bridges subject to strike-slip faulting

During earthquakes, the long-span railway bridges crossing active faults are more vulnerable because of the combined effects of pulsed ground motions and surface dislocations. To study the track-bridge deformation and interaction of long-span railway suspension bridges crossing the strike-slip faults, the refined finite element model of a ballasted track-bridge-pile-soil coupled system was established using the nonlinear finite element software ANSYS/LS-DYNA. A detailed and systematic numerical simulation was conducted from the soil cracking and compression during the ground surface rupture, pile–soil interaction, and three-dimensional track constraints to track-bridge deformation relationships and interactions. One-dimensional wave propagation theory was employed to derive the ground motions on the bedrock according to ground surface-measured seismic records. The influences of the fault-crossing angle (FCA) and permanent ground rupture displacement (PGRD) on the seismic responses and track-bridge interaction were analysed by considering the pile–soil interaction and site response effect. A method for calculating the track curvature radius based on track deformation is presented to evaluate the running traffic conditions of the trains. Additionally, the stability of the ballast bed was estimated using the track-bridge relative displacement. The conclusions drawn can be applied in practical seismic design and train running safety assessment of long-span railway suspension bridges crossing the strike-slip faults.

Appearing shock waves in Arruda – Boyce incompressible rod

The Arruda – Boyce incompressible hyperelastic potentials are used for analyzing one-dimensional acoustic wave propagation in a semi-infinite nonlinearly elastic rod. It has been found that during the propagation of the delta-like pulses, the following phenomena are observed, (i) the shock wave fronts arise; (ii) the pulses spread out due to physical dispersion; (iii) the mechanical energy of the considered system decreases with time, resulting in a decrease of the pulse magnitudes; and, at the same time (iv) thermal energy arises and increases with time, that is caused by formation and propagation of shock wave fronts. The analysis utilizes a combined method consisting of the explicit time integration technique coupled with the finite element method for spatial discretization.

Direct spatio-temporal stress field determination combining full-field deformation measurements and explicit finite element method: Concept verification

High strain rate loading of materials with spatially heterogeneous properties produces non-homogeneous and transient stress-strain states. Such stress-strain states are atypical of classical split Hopkinson pressure bar (SHPB) analysis that assumes homogeneous deformation and dynamic force equilibrium. To determine spatio-temporal stress fields in heterogeneous materials, a novel concept combining digital image correlation (DIC) full-field deformation measurements and explicit dynamic finite element method (EFEM) is described in this paper. The concept utilizes measured boundary forces and DIC measurements including both displacements and accelerations as input. The measured input is used to calculate internal forces, and hence the stress fields, within each continuum finite element by solving the governing equations of motion using the framework of EFEM. The DIC+EFEM concept procedure is verified using simulated synthetic data considering one-dimensional stress wave propagation in a bar. The reconstructed axial stress fields match identically with the exact EFEM solution for both homogeneous and heterogeneous materials that are elastic or elastic-plastic. The influence of DIC measurement noise on the reconstructed stresses is also studied.